Multi-dimensional scalar balance laws with discontinuous flux
نویسندگان
چکیده
منابع مشابه
A BGK approximation to scalar conservation laws with discontinuous flux
We study the BGK approximation to first-order scalar conservation laws with a flux which is discontinuous in the space variable. We show that the Cauchy Problem for the BGK approximation is well-posed and that, as the relaxation parameter tends to 0, it converges to the (entropy) solution of the limit problem.
متن کاملWell-posedness for Multidimensional Scalar Conservation Laws with Discontinuous Flux
We obtain a well-posedness result of an entropy solution to a multidimensional scalar conservation law with discontinuous (quasi-homogeneous) flux satisfying crossing conditions, but with no genuine nonlinearity assumptions. The proof is based on the kinetic formulation of the equation under consideration and it does not involve any transformation of the original equation or existence of strong...
متن کاملProper Entropy Conditions for Scalar Conservation Laws with Discontinuous Flux
By discovering that solutions of the vanishing viscosity approximation (but without flux regularization) to a scalar conservation law with discontinuous flux are equal to a flux crossing point at the interface, we derive entropy conditions which provide well-posedness to a corresponding Cauchy problem. We assume that the flux is such that the maximum principle holds, but we allow multiple flux ...
متن کاملEntropy conditions for scalar conservation laws with discontinuous flux revisited
We propose new entropy admissibility conditions for multidimensional hyperbolic scalar conservation laws with discontinuous flux which generalize one-dimensional Karlsen-Risebro-Towers entropy conditions. These new conditions are designed, in particular, in order to characterize the limit of vanishing viscosity approximations. On the one hand, they comply quite naturally with a certain class of...
متن کاملConservation laws with discontinuous flux
We consider an hyperbolic conservation law with discontinuous flux. Such partial differential equation arises in different applicative problems, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic solutions...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2014
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2014.07.009